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Weight on other worlds

Gravity and orbits · level 2, lesson 3 of 6

A question to start

If your bathroom scale says 30 kg at home, what would it say on Mars? On the Moon? On Jupiter, if you could stand there?

The idea

Each world pulls with its own strength. We can write each one as a number compared with the Earth's pull: Earth is 1.

World Pull (Earth = 1) A bathroom scale that reads 30 kg on Earth would read
Earth 1 30 kg
Mars 0.38 11 kg
Moon 0.17 5 kg
Jupiter (at its cloud tops) 2.5 76 kg

To find your reading on another world, multiply your Earth reading by that world's number. On Mars: \(30 \times 0.38 = 11.4\), about 11 kg.

Why is Mars's pull smaller? Mars has much less stuff in it than the Earth: about a tenth of the mass. But it is also about half as wide, so you stand closer to its middle, and that makes the pull stronger again. The two together give 0.38. (You will work this out yourself in level 6.)

The scale is fooled, by the way. It shows kilograms, but it is really measuring how hard you press on it. Your mass does not change on Mars; your weight does.

MoonMarsEarthJupiter 0.170.3812.5

Worked examples

1. A rover. Curiosity's mass is about 900 kg. On Mars, a scale under it would read \(900 \times 0.38 \approx 340\) kg. Its wheels carry a lot less load than they would at home, which is one reason a car-sized rover can roll on six thin wheels.

2. A backpack. An astronaut's suit and backpack might be 60 kg. On Mars that feels like 23 kg, about like carrying a big bag of potatoes on Earth.

Try it

  1. A dog weighs 20 kg on a bathroom scale on Earth. What would the scale show on Mars?
  2. What would the dog's scale show on the Moon?
  3. You read 11 kg on a scale on Mars. About what would it show on Earth?
  4. On which world in the table would you feel heaviest?
Answers
  1. \(20 \times 0.38 = 7.6\), about 8 kg.
  2. \(20 \times 0.17 = 3.4\), about 3 kg.
  3. Divide by 0.38: \(11 \div 0.38 \approx 29\), about 30 kg.
  4. Jupiter.

Common mistake

Multiplying the mass. On Mars your mass is still 30 kg. Only the scale reading (the weight) changes. When you multiply by 0.38, you are working out the pull, not shrinking the person.

Where it leads